Summary
We define the Boolean cost (or the bit-cost) of arithmetic computations, relate it to numerical stability of computations with finite precision and survey the major techniques available for estimating and decreasing it. We also study the related problem of reducing the arithmetic complexity (represented by the number of ops involved) of computing approximation to the output. We include some techniques from recent journal articles and technical reports and a new result on the numerical stability of FFT. Some of the results and the techniques have been or promise to be useful in practice of computing.
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© 1994 Springer Science+Business Media New York
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Bini, D., Pan, V.Y. (1994). Bit-Operation (Boolean) Cost of Arithmetic Computations. In: Polynomial and Matrix Computations. Progress in Theoretical Computer Science. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0265-3_3
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DOI: https://doi.org/10.1007/978-1-4612-0265-3_3
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6686-0
Online ISBN: 978-1-4612-0265-3
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